This function provides the analysis of regional economic sigma convergence (decline of deviation) for a time series using a trend regression
sigmaconv.t(gdp1, time1, gdp2, time2, sigma.measure = "sd", sigma.log = TRUE,
sigma.weighting = NULL, sigma.issample = FALSE,
sigma.plot = FALSE, sigma.plotLSize = 1, sigma.plotLineCol = "black",
sigma.plotRLine = FALSE, sigma.plotRLineCol = "blue",
sigma.Ymin = 0, sigma.plotX = "Time", sigma.plotY = "Variation",
sigma.plotTitle = "Sigma convergence", sigma.bgCol = "gray95", sigma.bgrid = TRUE,
sigma.bgridCol = "white", sigma.bgridSize = 2, sigma.bgridType = "solid",
print.results = FALSE)A numeric vector containing the GDP per capita (or another economic variable) at time t
A single value of time t (= the initial year)
A data frame containing the GDPs per capita (or another economic variable) at time t+1, t+2, t+3, ..., t+n
A single value of time t+1
argument that indicates how the sigma convergence should be measured. The default is output = "sd", which means that the standard deviation is used. If output = "var" or output = "cv", the variance or the coefficient of variation is used, respectively.
Logical argument. Per default (sigma.log = TRUE), also in the sigma convergence analysis, the economic variables are transformed by natural logarithm. If the original values should be used, state sigma.log = FALSE
If the measure of statistical dispersion in the sigma convergence analysis (coefficient of variation or standard deviation) should be weighted, a weighting vector has to be stated
Logical argument that indicates if the dataset is a sample or the population (default: is.sample = FALSE, so the denominator of variance is \(n\))
Logical argument that indicates if a plot of sigma convergence has to be created
If sigma.plot = TRUE: Line size of the sigma convergence plot
If sigma.plot = TRUE: Line color of the sigma convergence plot
If sigma.plot = TRUE: Logical argument that indicates if a regression line has to be added to the plot
If sigma.plot = TRUE and sigma.plotRLine = TRUE: Color of the regression line
If sigma.plot = TRUE: start value of the Y axis in the plot
If sigma.plot = TRUE: Name of the X axis
If sigma.plot = TRUE: Name of the Y axis
If sigma.plot = TRUE: Title of the plot
If sigma.plot = TRUE: Plot background color
If sigma.plot = TRUE: Logical argument that indicates if the plot contains a grid
If sigma.plot = TRUE and sigma.bgrid = TRUE: Color of the grid
If sigma.plot = TRUE and sigma.bgrid = TRUE: Size of the grid
If sigma.plot = TRUE and sigma.bgrid = TRUE: Type of the grid
Logical argument that indicates if the function shows the results or not
Returns a matrix containing the trend regression model and the resulting significance tests (F-statistic, t-statistic).
From the regional economic perspective (in particular the neoclassical growth theory), regional disparities are expected to decline. This convergence can have different meanings: Sigma convergence (\(\sigma\)) means a harmonization of regional economic output or income over time, while beta convergence (\(\beta\)) means a decline of dispersion because poor regions have a stronger economic growth than rich regions (Capello/Nijkamp 2009). Regardless of the theoretical assumptions of a harmonization in reality, the related analytical framework allows to analyze both types of convergence for cross-sectional data (GDP p.c. or another economic variable, \(y\), for \(i\) regions and two points in time, \(t\) and \(t+T\)), or one starting point (\(t\)) and the average growth within the following \(n\) years (\(t+1, t+2, ..., t+n\)), respectively. Beta convergence can be calculated either in a linearized OLS regression model or in a nonlinear regression model. When no other variables are integrated in this model, it is called absolute beta convergence. Implementing other region-related variables (conditions) into the model leads to conditional beta convergence. If there is beta convergence (\(\beta < 0\)), it is possible to calculate the speed of convergence, \(\lambda\), and the so-called Half-Life \(H\), while the latter is the time taken to reduce the disparities by one half (Allington/McCombie 2007, Goecke/Huether 2016). There is sigma convergence, when the dispersion of the variable (\(\sigma\)), e.g. calculated as standard deviation or coefficient of variation, reduces from \(t\) to \(t+T\). This can be measured using ANOVA for two years or trend regression with respect to several years (Furceri 2005, Goecke/Huether 2016).
This function calculates the standard deviation (or variance, coefficient of variation) for all GDPs per capita (or another economic variable) for the given years and executes a trend regression for these deviation measures. If the slope of the trend regression is negative, there is sigma convergence.
Allington, N. F. B./McCombie, J. S. L. (2007): “Economic growth and beta-convergence in the East European Transition Economies”. In: Arestis, P./Baddely, M./McCombie, J. S. L. (eds.): Economic Growth. New Directions in Theory and Policy. Cheltenham: Elgar. p. 200-222.
Capello, R./Nijkamp, P. (2009): “Introduction: regional growth and development theories in the twenty-first century - recent theoretical advances and future challenges”. In: Capello, R./Nijkamp, P. (eds.): Handbook of Regional Growth and Development Theories. Cheltenham: Elgar. p. 1-16.
Dapena, A. D./Vazquez, E. F./Morollon, F. R. (2016): “The role of spatial scale in regional convergence: the effect of MAUP in the estimation of beta-convergence equations”. In: The Annals of Regional Science, 56, 2, p. 473-489.
Furceri, D. (2005): “Beta and sigma-convergence: A mathematical relation of causality”. In: Economics Letters, 89, 2, p. 212-215.
Goecke, H./Huether, M. (2016): “Regional Convergence in Europe”. In: Intereconomics, 51, 3, p. 165-171.
Young, A. T./Higgins, M. J./Levy, D. (2008): “Sigma Convergence versus Beta Convergence: Evidence from U.S. County-Level Data”. In: Journal of Money, Credit and Banking, 40, 5, p. 1083-1093.
rca, sigmaconv, betaconv.nls, betaconv.speed, cv, sd2, var2
# NOT RUN {
data(G.counties.gdp)
# Loading GDP data for Germany (counties = Landkreise)
# Sigma convergence 2010-2014:
sigmaconv.t (G.counties.gdp$gdppc2010, 2010, G.counties.gdp[65:68], 2014,
sigma.plot = TRUE, print.results = TRUE)
# Using the standard deviation with logged GDP per capita
sigmaconv.t (G.counties.gdp$gdppc2010, 2010, G.counties.gdp[65:68], 2014,
sigma.measure = "cv", sigma.log = FALSE, print.results = TRUE)
# Using the coefficient of variation (GDP per capita not logged)
# }
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